Many North American breeds will go 16H or better. All North American breeds have wide variations in way of going within the breed. This means buying "breed" does not buy you same thing as in the Peruvian or Paso Fino (which are far more "internally consistent breeds" when it comes to gait).
This puts you in the place of the princess who has to kiss a lot of frogs before they find their prince!!!
Good luck in your search.